Abstract
Mobile robots are desired with resilience to safely interact with prior-unknown environments and finally accomplish given tasks. This paper utilizes instantaneous local sensory data to stimulate the safe feedback motion planning (SFMP) strategy with adaptability to diverse prior-unknown environments without building a global map. This is achieved by the numerical optimization with the constraints, referred to as instantaneous local control barrier functions (IL-CBFs) and goal-driven control Lyapunov functions (GD-CLFs), learned from perceptional signals. In particular, the IL-CBFs reflecting potential collisions and GD-CLFs encoding incrementally discovered subgoals are first online learned from local perceptual data. Then, the learned IL-CBFs are united with GD-CLFs in the context of quadratic programming (QP) to generate the safe feedback motion planning strategy. Rather importantly, an optimization over the admissible control space of IL-CBFs is conducted to enhance the solution feasibility of QP. The SFMP strategy is developed with theoretically guaranteed collision avoidance and convergence to destinations. Numerical simulations are conducted to reveal the effectiveness of the proposed SFMP strategy that drives mobile robots to safely reach the destination incrementally in diverse prior-unknown environments.
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Data and materials used are available by contacting the corresponding author.
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References
Hudson, N., Talbot, F., Cox, M., Williams, J., Hines, T., Pitt, A., Wood, B., Frousheger, D., Surdo, K.L., Molnar, T., et al.: “Heterogeneous ground and air platforms, homogeneous sensing: Team csiro data61’s approach to the darpa subterranean challenge.” Preprint at arXiv:2104.09053 (2021)
LaValle, S.M.: Planning algorithms. Cambridge university press (2006)
Jaffar, M.K.M., Otte, M.: “Pip-x: Funnel-based online feedback motion planning/replanning in dynamic environments.” In: International Workshop on the Algorithmic Foundations of Robotics. Springer, pp. 132–148 (2022)
Majumdar, A., Tedrake, R.: Funnel libraries for real-time robust feedback motion planning. Int. J. Robot. Res. 36(8), 947–982 (2017)
Reist, P., Preiswerk, P., Tedrake, R.: Feedback-motion-planning with simulation-based lqr-trees. Int. J. Robot. Res. 35(11), 1393–1416 (2016)
Yershov, D.S., Frazzoli, E.: Asymptotically optimal feedback planning using a numerical hamilton-jacobi-bellman solver and an adaptive mesh refinement. Int. J. Robot. Res. 35(5), 565–584 (2016)
Agha-Mohammadi, A.-A., Chakravorty, S., Amato, N.M.: Firm: Sampling-based feedback motion-planning under motion uncertainty and imperfect measurements. Int. J. Robot. Res. 33(2), 268–304 (2014)
Lavalle, S.M., Konkimalla, P.: Algorithms for computing numerical optimal feedback motion strategies. Int. J. Robot. Res. 20(9), 729–752 (2001)
Claussmann, L., Revilloud, M., Gruyer, D., Glaser, S.: A review of motion planning for highway autonomous driving. IEEE Trans. Intell. Transp. Syst. 21(5), 1826–1848 (2019)
LaValle, S.M., Kuffner, J.J.: “Rapidly-exploring random trees: Progress and prospects: Steven m. lavalle, iowa state university, a james j. kuffner, jr., university of tokyo, tokyo, japan.” Algorithmic and computational robotics, pp. 303–307 (2001)
Tordesillas, J., Lopez, B.T., Everett, M., How, J.P.: Faster: Fast and safe trajectory planner for navigation in unknown environments. IEEE Trans. Robot. 38(2), 922–938 (2021)
Rimon, E., Koditschek, D.E.: “Exact robot navigation using artificial potential functions.” Departmental Papers (ESE) (1992)
Sunkara, V., Chakravarthy, A., Ghose, D.: Collision avoidance of arbitrarily shaped deforming objects using collision cones. IEEE Robot. Autom. Lett. 4(2), 2156–2163 (2019)
Tanner, H.G., Boddu, A.: Multiagent navigation functions revisited. IEEE Trans. Robot. 28(6), 1346–1359 (2012)
Mitchell, I.M., Bayen, A.M., Tomlin, C.J.: A time-dependent hamilton-jacobi formulation of reachable sets for continuous dynamic games. IEEE Trans. Autom. Control 50(7), 947–957 (2005)
Ames, A.D., Xu, X., Grizzle, J.W., Tabuada, P.: Control barrier function based quadratic programs for safety critical systems. IEEE Trans. Autom. Control 62(8), 3861–3876 (2016)
Zhao, H., Zeng, X., Chen, T., Liu, Z.: “Synthesizing barrier certificates using neural networks.” In: Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control, pp. 1–11 (2020)
Jin, W., Wang, Z., Yang, Z., Mou, S.: “Neural certificates for safe control policies,” Preprint at arXiv:2006.08465 (2020)
Jagtap, P., Pappas, G.J., Zamani, M.: “Control barrier functions for unknown nonlinear systems using gaussian processes.” In: 2020 59th IEEE Conference on Decision and Control (CDC), pp. 3699–3704 (2020)
Saveriano, M., Lee, D.: “Learning barrier functions for constrained motion planning with dynamical systems.” In: 2019 IEEE/RSJ International Conference on Intelligent Robots and System (IROS), pp. 112–119 (2019)
Robey, A., Hu, H., Lindemann, L., Zhang, H., Dimarogonas, D.V., Tu, S., Matni, N.: “Learning control barrier functions from expert demonstrations.” In: 2020 59th IEEE Conference on Decision and Control (CDC), pp. 3717–3724 (2020)
Srinivasan, M., Dabholkar, A., Coogan, S., Vela, P.A.: Synthesis of control barrier functions using a supervised machine learning approach. In: 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 7139–7145 (2020)
Freeman, R.A.: Robust control of nonlinear systems. University of California, Santa Barbara (1995)
Abate, A., Ahmed, D., Giacobbe, M., Peruffo, A.: Formal synthesis of lyapunov neural networks. IEEE Control Syst. Lett. 5(3), 773–778 (2020)
Capelli, B., Secchi, C., Sabattini, L.: “Passivity and control barrier functions: Optimizing the use of energy.” IEEE Robot. Autom. Lett. (2022)
Xiao, W., Belta, C.: High-order control barrier functions. IEEE Trans. Autom. Control 67(7), 3655–3662 (2021)
Xu, X.: Constrained control of input-output linearizable systems using control sharing barrier functions. Automatica 87, 195–201 (2018)
Grammatico, S., Blanchini, F., Caiti, A.: Control-sharing and merging control lyapunov functions. IEEE Trans. Autom. Control 59(1), 107–119 (2013)
Xiao, W., Cassandras, G.C., Belta, C.: Safety-critical optimal control for autonomous systems. J. Syst. Sci. Complex. 34(5), 1723–1742 (2021)
Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. Kdd, vol. 96, no. 34, pp. 226–231 (1996)
Rawlings, J.O., Pantula, S.G., Dickey, D.A.: Applied regression analysis: a research tool. Springer Science & Business Media (2001)
Holland, P.W., Welsch, R.E.: Robust regression using iteratively reweighted least-squares. Commun. Stat. - Theory Methods. 6(9), 813–827 (1977)
Xiao, W., Cassandras, C.G., Belta, C.A., Rus, D., “Control barrier functions for systems with multiple control inputs,” In: American Control Conference (ACC). IEEE, 2221–2226 (2022)
Team, M.S.C.: “Mobile robotics simulation toolbox.” [Online]. Available: https://github.com/mathworks-robotics/mobile-robotics-simulation-toolbox (2023)
Coleman, T., Branch, M.A., Grace, A.: “Optimization toolbox.” (1999)
Koenig, N., Howard, A.: “Design and use paradigms for gazebo, an open-source multi-robot simulator.” In: 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)(IEEE Cat. No. 04CH37566), vol. 3, pp. 2149–2154. IEEE (2004)
Quigley, M., Conley, K., Gerkey, B., Faust, J., Foote, T., Leibs, J., Wheeler, R., Ng, A.Y., et al.: “Ros: an open-source robot operating system.” In: ICRA workshop on open source software, vol. 3, no. 3.2, p. 5. Kobe, Japan (2009)
Fazil, M.: Ros autonomous slam using rapidly exploring random tree (rrt). [Online]. Available: https://github.com/fazildgr8/ros_autonomous_slam (2021)
Funding
This work was supported in part by the National Natural Science Foundation of China under Grant 62373123, and in part by the Fundamental Research Funds for the Central Universities under Grant WK2100000035.
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Cong Li contributed to the first draft of the manuscript and the development of the theoretical contributions. Zengjie Zhang contributed to the analysis and interpretation of the results. Nesrin Ahmed contributed to implementing the numerical validations. Qingchen Liu, Fangzhou Liu and Martin Buss supervised the study design, and reviewed, edited, and prepared the final version of the paper.
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Li, C., Zhang, Z., Ahmed, N. et al. Safe Feedback Motion Planning in Unknown Environments: An Instantaneous Local Control Barrier Function Approach. J Intell Robot Syst 109, 40 (2023). https://doi.org/10.1007/s10846-023-01962-8
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DOI: https://doi.org/10.1007/s10846-023-01962-8